Self-healing data
An introduction to consistency models, Quorums and CRDTs
Uwe Friedrichsen, codecentric AG, 2014-2015

@ufried
Uwe Friedrichsen | uwe.friedrichsen@codecentric.de | http://slideshare.net/ufried | http://ufried.tumblr.com

Why NoSQL?
• Scalability
• Easier schema evolution
• Availability on unreliable OTS hardware
• It‘s more fun ...

Why NoSQL?
• Scalability
• Easier schema evolution
• Availability on unreliable OTS hardware
• It‘s more fun ...

Challenges
• Giving up ACID transactions
• (Temporal) anomalies and inconsistencies
short-term due to replication or long-term due to partitioning
It might happen. Thus, it will happen!

C
Consistency
A
Availability
P
Partition Tolerance
Strict Consistency
ACID / 2PC
Strong Consistency
Quorum R&W / Paxos
Eventual Consistency
CRDT / Gossip / Hinted Handoff

Strict Consistency (CA)
• Great programming model
no anomalies or inconsistencies need to be considered
• Does not scale well
best for single node databases
„We know ACID – It works!“
„We know 2PC – It sucks!“
Use for moderate data amounts

And what if I need more data?
• Distributed datastore
• Partition tolerance is a must
• Need to give up strict consistency (CP or AP)

Strong Consistency (CP)
• Majority based consistency model
can tolerate up to N nodes failing out of 2N+1 nodes
• Good programming model
Single-copy consistency
• Trades consistency for availability
in case of partitioning
Paxos (for sequential consistency)
Quorum-based reads & writes

Quorum-based reads & writes
• N – number of nodes (replicas)
• R – number of reads delivering the same result required
• W – number of confirmed writes required
W > N / 2
R + W > N

Example 1
• 3 replica nodes
This is: N = 3
• W > N / 2 à W > 3 / 2 à W > 1,5
Let‘s pick: W = 2 (can tolerate failure of 1 node)
• R + W > N à R + 2 > 3 à R > 1
Let‘s pick: R = 2 (can tolerate failure of 1 node)

Client
Node 1
Node 3
Node 2

W
W
W
Client
Node 1
Node 3
Node 2

Client
Node 1
Node 3
Node 2
✔
✖
✔
W = 2
✔

Client
Node 1
Node 3
Node 2

R
R
R
Client
Node 1
Node 3
Node 2
✔
✔
✔

Client
Node 1
Node 3
Node 2
2x / 1x
✔
R = 2
✔

Client
Node 1
Node 3
Node 2

R
R
R
Client
Node 1
Node 3
Node 2
✔
✔
✖

Client
Node 1
Node 3
Node 2
1x / 1x
✖
R = 1
✖

Example 2
• 3 replica nodes
This is: N = 3
• W > N / 2 à W > 3 / 2 à W > 1,5
Let‘s pick: W = 3 (strict consistency – does not tolerate any failure)
• R + W > N à R + 3 > 3 à R > 0
Let‘s pick: R = 1 (single read from any node sufficient)

Example 3
• 5 replica nodes
This is: N = 5
• W > N / 2 à W > 5 / 2 à W > 2,5
Let‘s pick: W = 3 (can tolerate failure of 2 nodes)
• R + W > N à R + 3 > 5 à R > 2
Let‘s pick: R = 3 (can tolerate failure of 2 nodes)

Limitations of QB R&W
• Requires fixed set of replica nodes
Dynamic adding and removal of nodes not possible
• Client-centric consistency
Consistency only perceived on client, not on nodes
• Requires additional measures on nodes
Nodes need to implement at least eventual consistency
Use if client-perceived strong consistency is
sufficient and simplicity trumps formal precision

And what if I need more availability?
• Need to give up strong consistency (CP)
• Relax required consistency properties even more
• Leads to eventual consistency (AP)

Eventual Consistency (AP)
• Gives up some consistency guarantees
no sequential consistency, anomalies become visible
• Maximum availability possible
can tolerate up to N-1 nodes failing out of N nodes
• Challenging programming model
anomalies usually need to be resolved explicitly
Gossip / Hinted Handoffs
CRDT

Conflict-free Replicated Data Types
• Eventually consistent, self-stabilizing data structures
• Designed for maximum availability
• Tolerates up to N-1 out of N nodes failing
State-based CRDT: Convergent Replicated Data Type (CvRDT)
Operation-based CRDT: Commutative Replicated Data Type (CmRDT)

A bit of theory first ...

Convergent Replicated Data Type
State-based CRDT – CvRDT
• All replicas (usually) connected
• Exchange state between replicas, calculate new state on target replica
• State transfer at least once over eventually-reliable channels
• Set of possible states form a Semilattice
• Partially ordered set of elements where all subsets have a Least Upper Bound (LUB)
• All state changes advance upwards with respect to the partial order

Commutative Replicated Data Type
Operation-based CRDT - CmRDT
• All replicas (usually) connected
• Exchange update operations between replicas, apply on target replica
• Reliable broadcast with ordering guarantee for non-concurrent
updates
• Concurrent updates must be commutative

That‘s been enough theory ...

Counter

Op-based Counter
Data
Integer i
Init
i ≔ 0
Query
return i
Operations
increment(): i ≔ i + 1
decrement(): i ≔ i - 1

State-based G-Counter (grow only)
(Naïve approach)
Data
Integer i
Init
i ≔ 0
Query
return i
Update
increment(): i ≔ i + 1
Merge( j)
i ≔ max(i, j)

State-based G-Counter (grow only)
(Naïve approach)
R1
R3
R2
i = 1
U
i = 1
U
i = 0
i = 0
i = 0
I
I
I
M
i = 1
i = 1
M

State-based G-Counter (grow only)
(Vector-based approach)
Data
Integer V[] / one element per replica set
Init
V ≔ [0, 0, ... , 0]
Query
return ∑i V[i]
Update
increment(): V[i] ≔ V[i] + 1 / i is replica set number
Merge(V‘)
∀i ∈ [0, n-1] : V[i] ≔ max(V[i], V‘[i])

State-based G-Counter (grow only)
(Vector-based approach)
R1
R3
R2
V = [1, 0, 0]
U
V = [0, 0, 0]
I
I
I
V = [0, 0, 0]
V = [0, 0, 0]
U
V = [0, 0, 1]
M
V = [1, 0, 0]
M
V = [1, 0, 1]

State-based PN-Counter (pos./neg.)
• Simple vector approach as with G-Counter does not work
• Violates monotonicity requirement of semilattice
• Need to use two vectors
• Vector P to track incements
• Vector N to track decrements
• Query result is ∑i P[i] – N[i]

State-based PN-Counter (pos./neg.)
Data
Integer P[], N[] / one element per replica set
Init
P ≔ [0, 0, ... , 0], N ≔ [0, 0, ... , 0]
Query
Return ∑i P[i] – N[i]
Update
increment(): P[i] ≔ P[i] + 1 / i is replica set number
decrement(): N[i] ≔ N[i] + 1 / i is replica set number
Merge(P‘, N‘)
∀i ∈ [0, n-1] : P[i] ≔ max(P[i], P‘[i])
∀i ∈ [0, n-1] : N[i] ≔ max(N[i], N‘[i])

Non-negative Counter
Problem: How to check a global invariant with local information only?
• Approach 1: Only dec when local state is > 0
• Concurrent decs could still lead to negative value
• Approach 2: Externalize negative values as 0
• inc(negative value) == noop(), violates counter semantics
• Approach 3: Local invariant – only allow dec if P[i] - N[i] > 0
• Works, but may be too strong limitation
• Approach 4: Synchronize
• Works, but violates assumptions and prerequisites of CRDTs

Sets

Op-based Set
(Naïve approach)
Data
Set S
Init
S ≔ {}
Query(e)
return e ∈ S
Operations
add(e) : S ≔ S ∪ {e}
remove(e): S ≔ S {e}

Op-based Set
(Naïve approach)
R1
R3
R2
S = {e}
add(e)
S = {}
S = {}
S = {}
I
I
I
S = {e}
S = {}
rmv(e)
add(e)
add(e)
add(e)
rmv(e)
add(e)
S = {e}
S = {e}
S = {e}
S = {}

State-based G-Set (grow only)
Data
Set S
Init
S ≔ {}
Query(e)
return e ∈ S
Update
add(e): S ≔ S ∪ {e}
Merge(S‘)
S = S ∪ S‘

State-based 2P-Set (two-phase)
Data
Set A, R / A: added, R: removed
Init
A ≔ {}, R ≔ {}
Query(e)
return e ∈ A ∧ e ∉ R
Update
add(e): A ≔ A ∪ {e}
remove(e): (pre query(e)) R ≔ R ∪ {e}
Merge(A‘, R‘)
A ≔ A ∪ A‘, R ≔ R ∪ R‘

Op-based OR-Set (observed-remove)
Data
Set S / Set of pairs { (element e, unique tag u), ... }
Init
S ≔ {}
Query(e)
return ∃u : (e, u) ∈ S
Operations
add(e): S ≔ S ∪ { (e, u) } / u is generated unique tag
remove(e):
pre query(e)
R ≔ { (e, u) | ∃u : (e, u) ∈ S } /at source („prepare“)
S ≔ S R /downstream („execute“)

Op-based OR-Set (observed-remove)
R1
R3
R2
S = {ea}
add(e)
S = {}
S = {}
S = {}
I
I
I
S = {eb}
S = {}
rmv(e)
add(e)
add(eb)
add(ea)
rmv(ea)
add(eb)
S = {eb}
S = {eb}
S = {ea, eb}
S = {eb}

More datatypes
• Register
• Dictionary (Map)
• Tree
• Graph
• Array
• List
plus more representations for each datatype

Garbage collection
• Sets could grow infinitely in worst case
• Garbage collection possible, but a bit tricky
• Only remove updates that can be deleted safely
and were received by all replicas
• Usually implemented using vector clocks
• Can tolerate up to n-1 crashes
• Live only while no replicas are crashed
• Can induce surprising behavior sometimes
• Sometimes stronger consensus is needed (Paxos, ...)

Limitations of CRDTs
• Very weak consistency guarantees
Strives for „quiescent consistency“
• Eventually consistent
Not suitable for high-volume ID generator or alike
• Not easy to understand and model
• Not all data structures representable
Use if availability is extremely important

Further reading
1. Shapiro et al., Conflict-free Replicated
Data Types, Inria Research report, 2011
2. Shapiro et al., A comprehensive study
of Convergent and Commutative
Replicated Data Types,
Inria Research report, 2011
3. Basho Tag Archives: CRDT,
https://basho.com/tag/crdt/
4. Leslie Lamport,
Time, clocks, and the ordering of
events in a distributed system,
Communications of the ACM (1978)

Wrap-up
• CAP requires rethinking consistency
• Strict Consistency
ACID / 2PC
• Strong Consistency
Quorum-based R&W, Paxos
• Eventual Consistency
CRDT, Gossip, Hinted Handoffs
Pick your consistency model based on your
consistency and availability requirements

The real world is not ACID
Thus, it is perfectly fine to go for a relaxed consistency model

@ufried
Uwe Friedrichsen | uwe.friedrichsen@codecentric.de | http://slideshare.net/ufried | http://ufried.tumblr.com